If the square has been plotted in a graph, you can go about finding the diagonal of it by measuring the midpoint.
(1) Find the coordinates of the vertices of the square
(2) Use the coordinates of two vertices that are across from each other. Plug them into the midpoint equation: (X1 + X2)/2 , (Y1 + Y2)/2, and use your answers as the coordinates of the midpoint (x,y)
(3) Draw a straight line crossing through the midpoint from one opposite vertex to another. That is your diagonal.
Use Pythagoras on the triangle formed by two adjacent sides and the diagonal between their other ends: diagonal = √(122 + 122) = 12 x √2 ~= 16.97 units
A square with a perimeter of 120 units would have sides measuring 30 units each.
They came from geometry. If you have a square whose sides are 1 unit long then its diagonal is sqrt(2) units long.
If the length of a side of the square is S units then the diagonal is S*sqrt(2) units in length.
The diagonal is 33.941 units.
Not necessarily. If the sides are a multiple of sqrt(2) units, then the diagonal is rational.
Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length). so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units. As a square has sides of equal length the square on one side is actually the area of the square. i.e. the area of a square with a diagonal of 10 units is 50 square units. or generically the area of a square with a diagonal of length 'x' = (x2)/2
Using the quick method, it is 5√2
Use Pythagoras on the triangle formed by two adjacent sides and the diagonal between their other ends: diagonal = √(122 + 122) = 12 x √2 ~= 16.97 units
A square with a perimeter of 120 units would have sides measuring 30 units each.
The diagonal is ~16.97 units.
If the length of a side of the square is S units then the diagonal is S*sqrt(2) units in length.
They came from geometry. If you have a square whose sides are 1 unit long then its diagonal is sqrt(2) units long.
The diagonal is 33.941 units.
A = 18 square units.
The diagonal is 60*sqrt(2) = 84.853 units.
About 84.85 units.